681306 ÷ 13 
The aim is to understand the frequency of 13 in 681306.

Step 1:
6 divided by 13 is 0 with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Take the next digit (8) from the dividend and append it to 6, then repeat: 68 / 13

Moving on to step 2:
When dividing 68 by 13, we get 5 with a remainder of 3.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtracting 65 from 68 leaves us with 3.
Append the next digit (1) from the dividend to 3 and continue with: 31 / 13

Moving on to step 3:
31 divided by 13 is 2 with a remainder of 5.
Put 2 as the next digit of the answer. 
Result so far: 52.0
If we subtract 26 from 31, we get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 13

Going ahead to step 4:
13 can be fit into 53 4 times, resulting in a remainder of 1.
The number 4 becomes the next digit in our result. 
Result so far: 524.0
The remainder is 1 after subtracting 52 from 53.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 13

On to step 5:
10 divided by 13 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 5240.0
If we take 0 away from 10, we end up with 10.
Append the next digit (6) from the dividend to 10 and continue with: 106 / 13

Step 6:
13 goes into 106 8 times with a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 52408.0
If we subtract 104 from 106, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 7:
The number 13 fits into 20 1 times, leaving a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 52408.1
Subtracting 13 from 20 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 8:
The number 13 fits into 70 5 times, leaving a remainder of 5.
The next digit of our result is 5. 
Result so far: 52408.15
The remainder is 5 after subtracting 65 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 9:
13 goes into 50 3 times with a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 52408.153
If we subtract 39 from 50, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 10:
When dividing 110 by 13, we get 8 with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 52408.1538
Subtracting 104 from 110 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 11:
60 divided by 13 is 4 with a remainder of 8.
The next digit of our result is 4. 
Result so far: 52408.15384
Subtract 52 from 60 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 12:
13 can be fit into 80 6 times, resulting in a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 52408.153846
Subtracting 78 from 80 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 13:
The number 13 fits into 20 1 times, leaving a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 52408.1538461
If we take 13 away from 20, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 14:
13 can be fit into 70 5 times, resulting in a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 52408.15384615
Subtracting 65 from 70 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The final outcome is 52408.15384615, with a leftover of 5e-09.